Given the following notations, write a formula for x, the break-even sales level.
SP = selling price per unit
FC = total fixed cost
VC = variable cost per unit
x =

The break-even sales level \( x \) is the point where total revenue equals total costs. Using the given notations:

- \( SP \) = selling price per unit,
- \( FC \) = total fixed cost,
- \( VC \) = variable cost per unit,
- \( x \) = number of units sold (break-even point).

### Formula for the break-even point:
At the break-even point:
\[
\text{Total Revenue} = \text{Total Costs}
\]

Total Revenue is:
\[
SP \times x
\]

Total Costs are the sum of fixed costs and variable costs:
\[
FC + VC \times x
\]

Setting the two equal to each other:
\[
SP \times x = FC + VC \times x
\]

Now, solve for \( x \):
\[
SP \times x - VC \times x = FC
\]
\[
x(SP - VC) = FC
\]
\[
x = \frac{FC}{SP - VC}
\]

Thus, the break-even sales level is:
\[
x = \frac{FC}{SP - VC}
\]

### This is the formula for the break-even sales level.

Would you like any further explanation or details on how this formula works?

Here are 5 related questions:
1. How do changes in the selling price affect the break-even point?
2. What happens to the break-even point if the variable cost per unit increases?
3. Can you calculate the break-even sales level if given specific values for SP, VC, and FC?
4. How does the break-even formula adjust for multiple products with different prices and costs?
5. What is the relationship between contribution margin and the break-even point?

**Tip:** Always ensure that the selling price is greater than the variable cost; otherwise, the business will incur a loss for each unit sold.

Given the following notations, write a formula for x, the break-even sales level. SP = selling price per unit, FC = total fixed cost, VC = variable cost per unit.

Learn how to calculate the break-even sales level using the formula x = FC / (SP - VC). Understand key concepts such as total fixed costs (FC), selling price per unit (SP), and variable cost per unit (VC) with this step-by-step guide. Perfect for students in Grades 9-12.

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